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Research
54,360+ open-access research outputs.
We introduce a refined immersed boundary (IB) methodology that is better-than-first-order accurate in practice, while preserving key properties of "continuous-forcing" IB approaches that retain a sing…
For a graph \(G\), let $avm(G)$ denote the average size of its maximal matchings. This parameter was introduced by Engbers and Erey in the study of extremal problems for maximal matchings, and they as…
This work investigates minimal parametric networks in hyperspaces of closed subsets of metric spaces endowed with the Hausdorff distance. It is shown that the problems of finding such networks are non…
We show that every minimally generically globally rigid graph in $\mathbb R^d$ which contains a subgraph isomorphic to $K_{d+2}$ is itself isomorphic to $K_{d+2}$, confirming a conjecture by Garamv{\"…
We derive a sharp upper bound on the residuals produced by the flexible GMRES (FGMRES) method. The bound shows that FGMRES exhibits two phases of convergence depending on the residual tolerance of the…
We investigate the unique stationary measure of a positive recurrent reflecting Brownian motion in the upper half-plane, where the direction of reflection is constant on each half-axis. The Laplace tr…
We show that the VC-density in certain theories of oriented abelian groups is at most the size of parameter variables, which yields dp-minimality. We further prove that the VC-density of formulas in p…
We study solution discovery, where the goal is to obtain a feasible solution to a problem from an initial configuration by a bounded sequence of local moves. In many applications, however, the graph t…
We construct a Lagrangian Floer homology whose chain complex is generically generated by the inscriptions of isosceles trapezoids in a smooth Jordan curve. This is an extension of Greene and Lobb's Jo…
We develop a harmonic gauge on the space of Riemannian metrics and study its role in the variational and flow-theoretic structure of geometric analysis. We prove that the harmonic gauge eliminates div…
We address the question of the large-time behavior of solutions to reaction-diffusion equations in periodic media. We start with the description of the asymptotic shape of the invasion set, which is c…
Let $F$ be a finite field of odd characteristic. We prove that any set $A\subset F$ with $|A|\geq C|F|^{5/6}$ contains a nontrivial quadratic progression $(x, x+y, x+y^2), y\neq 0.$ For prime fields, …
We obtain estimates of the modulus of continuity for the real part of the Cauchy-type integral in the closure of domain bounded by an Ahlfors-regular integration curve. These estimates are more exact …
We study stochastic differential equations on the $d$-dimensional flat torus $\mathbb{T}^d$ with drift and perturbation coefficients in $L^{\infty}(\mathbb{T}^d;\mathbb{R}^d)$ and additive non-degener…
We consider a linearized inverse scattering problem for elastic waves. We prove that a fully anisotropic perturbation of the elastic parameters around an isotropic and homogeneous reference can be uni…
This paper investigates the continuous-time counterpart of the Q-function for entropy-regularized mean-field control (MFC) with controlled common noise, coined as q-function by Jia and Zhou (2023) in …
We study properties of the following four classes of operators on the Fock space in $\mathbb C^n:$ 1) weakly localized operators; 2) sufficiently localized operators in the sense of Xia and Zheng; 3) …
We consider series expansions in bases of classical orthogonal polynomials. When such a series solves a linear differential equation with polynomial coefficients, its coefficients satisfy a linear rec…
We prove pathwise convergence of the layerwise evolution of tokens in a finite-depth, finite-width transformer model with MultiLayer Perceptron (MLP) blocks to a continuous-time stochastic interacting…
The classification of maximal algebras of square block Toeplitz matrices is a considerably more difficult problem and has received relatively little attention in the existing literature. In this work,…
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